Jammed solids held together with pins: structure and dynamics*

Currently, much is known about idealized grains like soft discs in the vicinity of the "Point J" threshold for jamming. However, an important unanswered question concerns the role that a scaffolding in the form of fixed particles, or "pins", plays in the structure and dynamics of a jammed solid. We model pins as tiny fixed particles organized in lattice shapes such as square, triangular, honeycomb, or randomly distributed lattices. We find a number of interesting results: While at low pin densities the jamming threshold, φj, does what one expects - decreases linearly with pin density and independently of pin geometry - this is not true in general. Instead, the behavior of φj with pin density depends on the type of lattice, and whether the particles are bi- or polydisperse. The distribution of contact forces is very different from the familiar gaussian shape in the absence of pins. The linear elastic response is significantly affected by pins, both in terms of the magnitudes of bulk and shear moduli and the Zener ratio, showing that pins can break the isotropy of jammed states.